PDA

View Full Version : Differential forms as sections


Kreizhn
Nov16-10, 03:43 PM
Hey,

A quick question. In the definition of a differential form, we normally require that they be sections of the k-th exterior power of the cotangent bundle. However, on page 14 of Jurdjevic's book on Geometric Control Theory (http://books.google.ca/books?id=PpZXRUsBjgUC&printsec=frontcover&dq=geometric+control+theory&hl=en&ei=4vniTKyqLMSmngfwua2xDw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCwQ6AEwAA#v=onepage&q=differential%20form&f=false), he defines them simply as sections of the cotangent projection.

Is there a mistake in his notes or does this represent an alternative way of examining differential forms?

zhentil
Nov17-10, 10:40 AM
His definition is for 1-forms (covectors).

Kreizhn
Nov17-10, 11:26 AM
Ah, so do you mean to say that a when the "dimension" of the form is omitted, it should be assumed to be a 1-form?

zhentil
Nov17-10, 04:35 PM
That's not usual, no. I think the author was being sloppy.